after five hours...

With plenty of possibly incorrect assumptions that I still have to verify:

1. For a positive definite matrix A:
AXA' = A'XA
where X is also a matrix

*EDIT: OH noes... hindi pwede to!!! --> (pag-asa: is A symmetric?) --> buti na lang symmetric daw ang A! :D

2. For all matrices: --> OK: http://www.ltcconline.net/greenl/courses/203/MatricesApps/inverse.htm
(A^-1)(B^-1) = (AB)^-1

3. For all matrices also:
ABA^-1 = B

* can't find web page on this. Maybe I can argue that the result of A is a scalar.